Problem: $ \left(\dfrac{9}{100}\right)^{\frac{5}{2}}$
Solution: $= \left(\left(\dfrac{9}{100}\right)^{\frac{1}{2}}\right)^{5}$ To simplify $\left(\dfrac{9}{100}\right)^{\frac{1}{2}}$ , figure out what goes in the blank: $\left(? \right)^{2}=\dfrac{9}{100}$ To simplify $\left(\dfrac{9}{100}\right)^{\frac{1}{2}}$ , figure out what goes in the blank: $\left({\dfrac{3}{10}}\right)^{2}=\dfrac{9}{100}$ so $ \left(\dfrac{9}{100}\right)^{\frac{1}{2}}=\dfrac{3}{10}$ So $\left(\dfrac{9}{100}\right)^{\frac{5}{2}}=\left(\left(\dfrac{9}{100}\right)^{\frac{1}{2}}\right)^{5}=\left(\dfrac{3}{10}\right)^{5}$ $= \left(\dfrac{3}{10}\right)\cdot\left(\dfrac{3}{10}\right)\cdot \left(\dfrac{3}{10}\right)\cdot \left(\dfrac{3}{10}\right)\cdot \left(\dfrac{3}{10}\right)$ $= \dfrac{9}{100}\cdot\left(\dfrac{3}{10}\right)\cdot \left(\dfrac{3}{10}\right)\cdot \left(\dfrac{3}{10}\right)$ $= \dfrac{27}{1000}\cdot\left(\dfrac{3}{10}\right)\cdot \left(\dfrac{3}{10}\right)$ $= \dfrac{81}{10000}\cdot\left(\dfrac{3}{10}\right)$ $= \dfrac{243}{100000}$